The 5 pound (around US$10; Ђ7) increase will come into effect on June 13, raising the one-way surcharge on long-haul flights of less than nine hours to 38 pounds (around $76; euro45) and for flights longer than nine hours to 43 pounds (around US$85; euro63).
The increase comes just over a month after BA raised both charges by 3 pounds.
"The cost of fuel has again risen significantly in recent weeks," said Robert Boyle, British Airways' commercial director. "Unfortunately, we have little choice but to pass on some of this extra cost to our customers."
The carrier expects its fuel bill to be more than 2 billion pounds (US$4 billion; euro2.9 billion) this year.
The costs are mainly being passed on to long-haul passengers. The short-haul fuel charge remains unchanged at 8 pounds (US$16; euro12).